Problem: ${9 \div \dfrac{2}{3} =}$
${9} \div \dfrac{2}{3}} ={\dfrac{9}{1}} \div \dfrac{2}{3}} $ $~~~~~~~{\gray{\text{Rewrite 9 as }\dfrac{9}{1}}}. $ $\phantom{9 \div \dfrac{2}{3}}} ={\dfrac{9}{1}} \times \dfrac{3}{2}}$ $ ~~~~~~{\gray{\text{Multiply by reciprocal of }\dfrac{2}{3}.}} $ $\phantom{8 \div \dfrac{2}{3}}} ={\dfrac{{9}\times3}}{1\timesD2}} $ $~~~~~~~{\gray{\text{Multiply. }}} $ $\phantom{8 \div \dfrac{2}{3}}} ={\dfrac{27}{2}} $ ${9 \div \dfrac{2}{3} =\dfrac{27}{2}}$ [Wait, can we rewrite the answer as a mixed number?]